When Galileo revitalized Archimedes’ hydrostatics, he had to invent a scale that could transform the experiment into a number via two weighings: one in air and one in water. The precedents for his instrument were the water balance, the immersion aerometer, the pycnometer and a triple hydrostatic balance. The heart of the book is the dispute with the Florentine Aristotelians: this allowed Galileo to clarify hydrostatic ideas in a text that has now become a classic.